derivative of (9x^{3/2}/3)

Lösung

\frac{d}{d x} (\frac{9 x ^{\frac{3}{2}}}{3})

\frac{9 x ^{\frac{1}{2}}}{2}

Schritte zur Lösung

\frac{d}{d x} (\frac{9 x ^{\frac{3}{2}}}{3})

Vereinfache

\frac{9 x ^{\frac{3}{2}}}{3} : 3 x^{\frac{3}{2}}

= \frac{d}{d x} (3 x^{\frac{3}{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{\frac{3}{2}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

Vereinfache

3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{9 x ^{\frac{1}{2}}}{2}

= \frac{9 x ^{\frac{1}{2}}}{2}

s im pl i f y (a x^{2} + b x + c) e^{- \frac{x}{6}}

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